Jug measuring: Algorithms and complexity

被引:1
|
作者
Shieh, Min-Zheng [1 ]
Tsai, Shi-Chun [1 ]
机构
[1] Natl Chiao Tung Univ, Dept Comp Sci, Hsinchu 30050, Taiwan
关键词
Jug measuring problem; inapproximability; LLL algorithm; lattice problem;
D O I
10.1016/j.tcs.2008.01.003
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
We study the hardness of the optimal jug measuring problem. By proving tight lower and upper bounds on the minimum number of measuring steps required, we reduce an inapproximable NP-hard problem (i.e., the shortest GCD multiplier problem [G. Havas, J.-P. Seifert, The Complexity of the Extended GCD Problem, in: LNCS, vol. 1672, Springer, 1999]) to it. It follows that the optimal jug measuring problem is NP-hard and so is the problem of approximating the minimum number of measuring steps within a constant factor. Along the way, we give a polynomial-time approximation algorithm with an exponential error based on the well-known LLL basis reduction algorithm. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:50 / 62
页数:13
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